Encodings of Bounded Synthesis

  • Peter Faymonville
  • Bernd Finkbeiner
  • Markus N. Rabe
  • Leander TentrupEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10205)


The reactive synthesis problem is to compute a system satisfying a given specification in temporal logic. Bounded synthesis is the approach to bound the maximum size of the system that we accept as a solution to the reactive synthesis problem. As a result, bounded synthesis is decidable whenever the corresponding verification problem is decidable, and can be applied in settings where classic synthesis fails, such as in the synthesis of distributed systems. In this paper, we study the constraint solving problem behind bounded synthesis. We consider different reductions of the bounded synthesis problem of linear-time temporal logic (LTL) to constraint systems given as boolean formulas (SAT), quantified boolean formulas (QBF), and dependency quantified boolean formulas (DQBF). The reductions represent different trade-offs between conciseness and algorithmic efficiency. In the SAT encoding, both inputs and states of the system are represented explicitly; in QBF, inputs are symbolic and states are explicit; in DQBF, both inputs and states are symbolic. We evaluate the encodings systematically using benchmarks from the reactive synthesis competition (SYNTCOMP) and state-of-the-art solvers. Our key, and perhaps surprising, empirical finding is that QBF clearly dominates both SAT and DQBF.


Boolean Function Transition System Constraint System Synthesis Problem Atomic Proposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Peter Faymonville
    • 1
  • Bernd Finkbeiner
    • 1
  • Markus N. Rabe
    • 2
  • Leander Tentrup
    • 1
    Email author
  1. 1.Saarland UniversitySaarbrückenGermany
  2. 2.University of CaliforniaBerkeleyUSA

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